# Simple methods to determine powder flow property

Most commonly used testing method to determine powder flow – Hausner ratio, Angle of repose, and Compressibility index

**To get FREE Excel Sheet for calculation of powder flow property – Angle of repose, Compressibility index, and Hausner ratio, refer end section of the page.**

## What are the most widely used testing methods to determine powder flow?

There are following four commonly used methods:

(1) Compressibility index or Hausner ratio

(2) Angle of repose

(3) Shear cell

(4) Flow rate through an orifice

## What is Angle of Repose?

The angle of repose is a simple technique for estimating the powder flow properties.

## How to determine Angle of Repose?

**Step 1: ** Flow the powder through a funnel**Step 2: ** Powder should fall freely onto a fixed diameter base**Step 3: ** Measure height. Measure the diameter of the cone formed.

## What is calculation formula for Angle of Repose?

**tan Θ (Angle of repose) = h/r**

In this formula,

h = Powder cone height

r = Cone base radius

## Application of Angle of Repose

- Gives information regarding interparticulate friction between particles or information regarding resistance to movement between particles
- Used to determine flow properties of solids

## Method or Procedure for measurement of Angle of Repose

**What is recommendation on procedure or method according to USP <1174>?**

- Use fixed (vibration free) base. It should have a retaining lip. This will help to retain a powder layer on the base
- Adjust the height of the funnel. This should be done in such a way that it build up a symmetrical powder cone
- The height of the funnel should be adjusted carefully. It should maintain approximate height of 2-4 centimeter from the top of the powder pile
- Measuring the powder cone height (h) and radius of the base (r)
- Calculating the angle of repose using the give equation

## Angle of Repose and corresponding Scale of Flowability

Following information provides insight about powder flow properties and related Angles of Repose value:

Angle of Repose (degrees) | Flow Property |

Twenty five (25) to Thirty (30) | Excellent |

Thirty one (31) to Thirty five(35) | Good |

Thirty six (36) to forty (40) | Fair-aid not needed |

Forty one (41) to Forty five (45) | Passable-may hang up |

Forty six (46) to Fifty five(55) | Poor – must agitate, vibrate |

Fifty six (56) to Sixty five (65) | Very poor |

Sixty six (66)> | Very, very poor |

Based on various studies, when angle of repose is higher than 45°, there is high probability that it is not be suitable for tablet compression process. Addition of flowing agent will improve the flow property.

## Example calculation of Angle of Repose

Cone height (h) = 4 cm

Radius of the cone base is = 4.5 cm

tan ϴ = h/r = 4/4.5 = 0.88

arctan or tan^{-1} (0.88) = 41.63 degrees

## What is Compressibility index and what is Hausner Ratio?

**Definition of Compressibility index:**

The Compressibility Index is also called as Carr Compressibility Index. The index gives an idea of a powder tendancy that needs to be compressed.

It gives idea that about how powder will settle and interparticulate interactions.

**Definition of Hausner Ratio:**

Unlike the Carr Compressibility Index, this index also gives an estimation of the tendency of a powder that needs to be compressed and interparticulate interactions.

The ratio is named after the engineer, Henry H. Hausner. The value correlates to the granules or powder flowability.

- Fast, Simple, and popular to predicting flow characteristics of powder
- The Hausner ratio and compressibility index are indirect measure of:

o Bulk density

o Size and shape

o Cohesiveness of materials

o Moisture content

o Surface area

- The Hausner ratio and compressibility index can be determined by calculating, the tapped volume and the bulk volume of a powder as follows:

In the formula,

V_{o} – Unsettled apparent volume

V_{f} – Final tapped volume

- Alternatively, the compressibility index and Hausner ratio can be calculated using bulk density (ρ
_{bulk}) and tapped density (ρ_{tapped}) of a powder as follows:

In the formula,

ρ _{bulk} – bulk density

ρ _{tapped} – tapped density

Scale of flowability based on the Hausner ratio and compressibility index is given below.

Compressibility Index (%) | Flow Character | Hausner Ratio |
---|---|---|

<10 | Excellent | 1.00–1.11 |

11–15 | Good | 1.12–1.18 |

16–20 | Fair | 1.19–1.25 |

21–25 | Passable | 1.26–1.34 |

26–31 | Poor | 1.35–1.45 |

32–37 | Very poor | 1.46–1.59 |

>38 | Very, very poor | >1.60 |

## Procedure to determine Compressibility Index as well as Hausner Ratio

Required weight of sample: 100 g

Size of volumetric dry graduated cylinder: 250 mL

- Introduce material (approximately 100 g of test sample, M,) to be analyzed into a cylinder (least count of 2 mL). Do not compact.
- Level the powder (V
_{0}) to the nearest graduated unit. Ensure powder does not get compacted. - Calculate the bulk density in g/mL (ρ
_{ bulk}) by the formula m/V_{0 }. - Fix the cylinder in the cylinder holder.
- Carry out following taps on the same powder sample:

10 taps and read the resultant volumes V10

500 taps and read the corresponding volumes V500

1250 taps and read the corresponding volumes V1250 - Read the nearest graduated unit and the difference between last two taps, which should be less than or equal to 2 mL.
- If the difference are more than 2 mL, repeat in increments such as 1250 taps. The repeation should be done until the difference between those last two measurements are less than or equal to 2 mL.
- Calculate the tapped density in g/mL (ρ
_{ tapped}). - Formula for tapped density is m/V
_{f}, in which V_{f }is the final tapped volume. - Calculate the Hausner ratio and Compressibility index using above formulas.